Scale object and preserve proportions
You could do it this way:


Create your star (10 vertices cylinder, scale 5 of them). Extrude it with altE > Region (Vertex Normals). Click the Offset Even option in the operator panel (bottom of the T panel in 2.9, bottom left box in 2.8).





Delete the faces with X > Faces.





Extrude all and again with altE > Region (Vertex Normals) and click the Offset Even option. You could as well use the Solidify modifier.